Munich Personal RePEc Archive
Phillips curve in a small open economy:
A time series exploration of North
Cyprus
Islam, Faridul and Shahbaz, Muhammad and Shabbir,
Muhammad
COMSATS Institute of Information Technology, COMSATS
Institute of Information Technology, Woodbury School of Business
Utah Valley University
19 January 2011
Online at https://mpra.ub.uni-muenchen.de/28397/
MPRA Paper No. 28397, posted 25 Jan 2011 20:49 UTC
1
Phillips Curve in a Small Open Economy:
A Time Series Exploration of North Cyprus
Faridul Islam*
Department of Finance and Economics
Woodbury School of Business
Utah Valley University
Orem, UT 84058-5999
Email: [email protected]
Phone: 801-863-8858
Muhammad Shahbaz
Research Fellow, Centre for Research,
Department of Management Sciences,
COMSATS Institute of Information Technology,
Defense Road, Off Raiwind Road, Lahore, Pakistan
Muhammad Shahbaz Shabbir
Head, Centre for Research,
Department of Management Sciences,
COMSATS Institute of Information Technology,
Defense Road, Off Raiwind Road, Lahore, Pakistan
*Correspondence author: Faridul Islam, Department of Finance and Economics
Utah Valley University, Orem, UT 84058-5999, Email: [email protected]
Phone: 801-863-8858, Fax : 801-863-7218
2
Abstract:
The paper explores the existence and the stability of Phillips curve for North Cyprus, a
small developing economy, using time series data. ADF unit root test is employed to
check for stationarity. ARDL and DOLS approaches to cointegration have been used to
explore the long run relation and ECM to understand short run dynamics. The predictive
properties DOLS are better than those of the conventional methods. The estimates point
to the existence of Phillips curve both in the long and the short run. CUSUM and
CUSUMsq tests confirm a stable relation.
Key Words: Inflation, Unemployment, ADF, Cointegration, DOLS
JEL Classification: E31, E24, C22
3
I. Introduction
The observed inverse relationship between nominal wages changes and unemployment
rates with the British data over the period 1861-1957, first discovered by Phillips (1958)
has come to be known as the Phillips Curve. Since then, a sizeable theoretical and
empirical literature have backed up a stable trade off between these series [Lipsey (1960),
Phelps (1967), Leijonhufvud (1968), Samuelson and Solow (1970), Solow (1970) and
Gordon (1971)]. The possibility of a trade off offers policymakers a tool to deal with
macroeconomic disequilibrium. However, the failure to explain economic crises of the
1970s had cast serious doubts about the validity of the relation. In particular, Phelps
(1967), Friedman (1968), Lucas (1976) and Okun (1975) argued against the hypothesis.
A few papers lent support to a stable non linear relation [Onder (2004), Kustepeli (2005),
Furuoka (2007), Tang and Lean (2007), Schreiber and Wolters (2007), Dammak and
Boujelbene (2009)]. Others found an unstable relation between unemployment and
inflation [Lucas (1972, 1973, 1976); Okun (1975); Turner (1997); Atkeson and Ohanian
(2001); Niskanen (2002); Demers (2003) and Reichel (2004)]. These studies used cross
sectional, time series and panel data sets.
The topic deserves closer scrutiny because macro models invoke fixed non-accelerating
inflation rate of unemployment (NAIRU) as the long-run approach. All NAIRU models
postulate a vertical long-run Phillips curve implying no trade off in the long-run.
Persistently rising unemployment rate among European nations has rendered a fixed
NAIRU unrealistic. However, the search for a relation using sophisticated econometric
techniques with time-varying coefficients as in Gordon (1997) continued. The question of
4
endogeneity from mutual dependence of the variables led to fresh attempts at reinventing
the relation. Against the backdrops, researchers began to check for reverse causality.
Akerlof et al. (1996, 2000), Karanassou et al. (2005), and Holden (2004) discuss models
in which long-run trade-off between output and inflation can exist if the inflation rates are
low. Karanassou et al. (2003) provides support to a long-run inflation-unemployment
trade-off for some EU countries; and Franz (2005) for German. Thus whether or not a
long-run inflation-unemployment trade-off exists should be left to empirical tests using
appropriate tools. This may help clarify some of the mysteries that underline the
relationship between inflation and unemployment (Mankiw, 2001).
The objective of the paper is to explore the existence of Phillips curve and examine its
nature and stability for north Cyprus. Much of the earlier literature on Phillips curve has
examined the developed nations. The focus on the developing nations is relatively recent
[see literature review]. In an increasingly globalized world, sound macroeconomic policy
is considered critical for pursuing economic growth. This is more relevant for small open
economies which are vulnerable to major shocks. From that perspective the choice of
North Cyprus in this paper seems relevant. Figure 1 justifies further empirical exploration
of a Phillips curve for North Cyprus. The authors are not aware of any study purporting
to explore existence and stability of Phillips curve for North Cyprus. The research thus
fills a gap in knowledge and thus contributes to the literature. In this paper we implement
a variety of econometric tools to annual data from 1978–2007. To examine the long run
relation between inflation and unemployment rates the paper applies the ARDL bounds
5
testing approach to cointegration by Pesaran et al (2001). Given the size of the sample
ARDL appears appropriate. Dynamic ordinary least squares (DOLS) and OLS have also
been applied to explore the nature of the Phillips curve over time. The Error Correction
Model (ECM) captures the short run dynamics. Stability of the Phillips curve has been
checked by CUSUM and CUSUMsq recursive regression residuals based tests.
Figure 1 about here
The rest of study is organized as follows. Literature review is discussed in Section II.
Section III describes data sources and the empirical framework. Findings are discussed in
section IV. Conclusions and policy implication are drawn in Part V.
2. Literature Review
Although the Phillips relation was viewed simply as an empirical phenomenon, Lipsey
(1960) was the first to offer a theoretical foundation. Lipsey’s idea was subsequently
extended which came to be known as the augmented Phillips curve wherein Lucas added
an expected inflation component to the original specification. This model was tested
using the rational expectations hypothesis. This work later spearheaded the formation of a
group of economist under the banner of ‘new classical economists’; and also opened up a
debate over the shape of the ‘aggregate supply curve for the economy’.
The possibility of a trade-off between inflation and unemployment was deemed important
from policy perspectives and drew substantial academic interest. This culminated in the
6
proliferation of a bourgeoning literature [see Santomero and Seater, 1979 for review of
earlier research]. Solow (1970) and Gordon (1971) showed Philips relation for the US
economy which is known as the “Solow-Gordon confirmation of the Phillips curve.”
The Philips curve fell from grace of the academicians during the 1980’s. Okun (1975)
notes that in the US, since the 1970s Phillips curve has become "an unidentified flying
object" (p. 353). The topic staged a comeback in the 1990’s as sophisticated econometric
tools became available. For example, Alogoskoufis and Smith (1991) found support to
Lucas (1976). Using US post-war macroeconomic data, King and Watson (1994) did not
find a relation1. Hogan, (1998) found low inflation rates with declining unemployment
rate concomitant with a lower level of NAIRU. The resulting low inflation might have
been from reduced import cost due to strong dollar which acted as a price shock.
DiNardo and Moore (1999) employed panel approach to OECD countries using OLS and
GLS methods and found the Philips relation, which is also corroborated by Malinov and
Somthers (1997), and Turner and Seghezza (1999). The later paper used Seemingly
Unrelated Estimation (SURE) method. Eliasson (2001) specified linear Phillips curve for
Sweden, Australia, and the United States and checked for parameters stability. They did
not find the Phillips curve for Australia and Sweden, but found one for the US.
Niskanen (2002) points out that in its common form the Phillips curve is misspecified and
that the long-run Phillips curve is positively sloped which may be due to lack of indexed
1 King and Watson (1994) conclude that Phillips curve will be in long-run and short-run if noises for both
periods are removed from the series of data.
7
tax code. Batini et al. (2000, 2005) analysis indicates that not only structural changes but
also labor markets and favorable supply shocks seem to affect inflation in the long run. In
the short run, changes in unemployment rate explain variations in inflation for UK. Gali
et al. (2001, 2005), and Rudd and Whelan (2005) used GMM approach but failed to find
strong Phillips relation. Reichel (2004) applied cointegration method to the industrialized
economies but found trade-off only for the US and Japan. Using quarterly data Dua and
Gaur (2009) found a forward-looking Phillips (not backward looking) for Japan, Hong
Kong, Korea, Singapore, Philippines, Thailand, China and India.
Lipsey (1960) found an inverse relation for Britain for 1914-18, but not after the War.
Turner (1997) argues that structural break since the 1970s in Britain may have caused the
instability of the Phillips curve. He emphasizes more on the stability, than its existence.
Atkeson and Ohanian (2001) also support Turner. Hansen and Pancs (2001) found
inverse relation between the series for Lativa. Bhanthumnavin (2002) finds the Phillips
curve for Thailand, but only in the post 1997 Asian flu. Graham and Snower (2002)
demonstrate a stable Phillips curve for Chile. They argue that the trade off in long run is
due to inter-relation between money growth and rise in nominal wages. Furuoka (2007)2
found relation between inflation and unemployment for Malaysia, which was later
confirmed by Tang and Lean3 (2007). The authors used Stock-Watson procedure.
Schreiber and Wolters (2007) applied VAR cointegration approach and found a long run
relation for German. Islam et al. (2003) revisit the US Philips relation using 1950-99 data
but did not find a strong relation.
2 Uses unemployment gap as proxy of unemployment
3 Uses consumer price index (CPI) for inflation
8
Furher (1995) notes that the Phillips relation has been robust and remained stable over the
past 35 years. Demer, (2003) uses Markov-switching model to Canada but did not find a
significant relation. Hart (2003) argues that Phillips curve has been vital in explaining
economic theory and empirical results. He used British hourly wage rate as proxy for
inflation. Scheibe and Vines 2005 found a trade off relation after reforms in China. They
use quarterly data, adjusted for structural change and found a vertical long-run Phillips4 curve.
They recommend exchange rate liberalization in China. Ogbokor, (2005) finds stagflation in
Namibia over the period of 1991–2005.
Cruz-Rodriguez (2008) found Phillips curve for Dominican Republic. However, the link
with output gap is positive, which may be due to world oil prices and exchange rate.
Whatever the effect, it was small. Del Boca et al. (2008) found Phillips curve for Italy for
1861-1998. The paper captures the effects of structural changes and asymmetries on the
estimates of the trade-off relation. In Italy a trade-off exists only during low inflation and
stable aggregate supply. Russell and Banerjee (2008) investigate vertical Phillips curve
assuming non-stationarity in the series. They find positive relation between inflation and
unemployment rate in short run for the United States.
Onder (2004) and Kustepeli (2005) find Phillips curve for Turkey. Subsequently, Onder
(2009) used structural break and Markov-switching models to examine the nature of
Phillips curve and finds a non-linear relation. The results point to absence of symmetry in
the inflation response to output gap. Dammak and Boujelbene (2009) find linear tradeoff
4 Output gap, the exchange rate, and inflation expectations play important roles in inflation
9
for Tanzania. Paul5 (2009) argues that droughts, oil shocks and liberalization-policy of
the early 1990s may be the reason for the absence of a Phillips curve in India. After
adjusting for the shocks he finds the Phillips curve suggesting a short-run tradeoff
between inflation and industrial output for India.
To complete the literature review, we bring in the latest strand in understanding the
inflation and unemployment relation. One branch of the literature models inflation
dynamics and estimates the unemployment rate as being compatible with inflation
stability. However, the other branch determines the real economic factors that drive the
natural rate of unemployment. Proponents of the new Keynesian Phillips (NPC) curve
argue that frictional growth--the interplay between lags and growth--generates an
inflation unemployment tradeoff in the long run. They propose a framework, e.g., the
chain reaction theory (CRT) and argue that evolution of inflation and unemployment can
be jointly determined. The CRT approach also provides a synthesis of the traditional
structural macroeconometric models and the (structural) vector autoregressions.
There are two main types of dynamic macro models. First, the monetary macroeconomic
models with its main focus on inflation dynamics. Second, the labor macroeconomic
models which seek to explain the evolution of unemployment. The old school argues that
inflation-unemployment dynamics is part of short run Phillips curve but in the long run
they are unrelated, rationalized within the classical dichotomy, where monetary policy
does not affect the real variables. This is consistent with the so-called natural rate of
unemployment (NRU) hypothesis. The NPC invokes “the presence of nominal frictions
5 Uses real GDP proxy for unemployment for India
10
and growing nominal variables (such as money, prices and wages), the real and monetary
sides of the economy cannot be compartmentalized in the long run.” Karanassou et al.
(2010, p. 2). “(They) argue that the phenomena of long-run economic growth and
business cycles cannot be compartmentalized either, as is done in the prevailing literature
where growth and cycles are analysed independently of one another. The interplay
between frictions (lagged adjustments) and growth we call frictional growth.” (ibid, p. 2)
3. Data and Methodology
The paper uses annual inflation and unemployment data to explore a long run relation for
the North Cyprus economy. The data covering 1978-2007 has been extracted from the
Social and Economic Indicators (2007) of the Turkish Republic of North Cyprus.
Researchers have included variables such as real GDP and marginal cost of production in
estimating Phillips curve. Gordon (1981) recommends using real gross national product
for unemployment rate. Proxy variables have been used for both unemployment rate and
inflation [Brouwer and Ericsson, 1998), Salman and Shukur, 2004]. Khalaf and Kichian
(2005) use output gap or real output as proxy for unemployment rate. To measure
inflation both CPI and PPI have been used. A limitation with the former is that it ignores
the producer side. Overall inflation rate is a better measure for inflation rate6 for an
economy. All variables are transformed in logarithms.
6 For variable and model specification, see Paul (2009), Alexis, (2008), Tang & Lean, (2007) Furuoka
(2007), Ogbokor (2005), Liew, (2004), Whelan (1997) and Lütkepohl (1991)
11
Before implementing cointegration technique, Augmented Dickey Fuller (ADF) method
is employed to test for stationarity of the series using Equation-1.
t
m
ttitt yyty εαδββ +∆+++=∆ ∑
=−−
1
1121 (1)
where, tε is a white noise process. Following the standard notations, we define:
)( 1−−=∆ ttt yyy,
)( 211 −−− −=∆ ttt yyy , )( 322 −−− −=∆ ttt yyy
In our search for a long run relation, we use cointegration approach. When variables are
cointegrated, the long-run relations are estimated by cointegrating vectors focusing on the
order of integration of each series. Johansen (1988a, 1991) derived distribution when the
cointegrated system is parameterized as a vector error correction model (VECM). For a
set of I(1) variables and a single cointegrating vector, Stock and Watson (1993) can be
applied. In this we regress any of the variables on the remaining contemporaneous levels
of the series and leads and lags of their first differences, and a constant. The method has
come to be known as the "dynamic OLS" (or GLS, as the case may be). The resulting
"dynamic OLS" (respectively GLS) estimators are asymptotically equivalent to the
Johansen estimator. In finite sample, these estimators perform better, relative to other
asymptotically efficient estimators, when simple short-run dynamics is involved.
The DOLS procedure requires partial knowledge of the series expected to cointegrate and
the orders of integration. With DOLS the problems associated with simultaneity,
endogeneity and serial correlation are resolved by including leads and lags in small
sample. The DOLS procedure is helpful if the series has different orders of lags (Stock-
Watson, 1993). In the case of normal distribution the estimators have desirable properties
12
as compared to Phillips and Perron (1988), Phillips and Loretan (1991) and Phillips and
Moon (1999, 2001). In particular, the Engle–Granger’s approach may not be satisfactory
if in a multivariate case more than one cointegrating vector is present (Seddighi et al.
2000). Engle-Granger estimator suffers from a non-standard asymptotic distribution.
Inferences on the parameters of the cointegrating vectors using DOLS estimator are
efficient. Monte Carlo studies by Agrawal (2001) favor DOLS in estimating the long run
relation. Predictive properties DOLS are better than the standard Engle-Granger (1987),
Johansen (1988, 1991); Johansen-Juselius (1990) and Phillips & Hansen (1990)
procedures. As such we also apply the DOLS using the following model.
t
k
pjjt
k
piit LunpLINFLUNPLINF εγγγγ +∆+∆++= ∑∑
±=−
±=− 4321
(1)
In Equation-4, 1γ refers to a constant and 2γ to the long run parameter. The number of
lags is denoted by p; k refers to lag length of the leads terms. The ε refers to the error
term. The selection of lags and leads is based on AIC.
In traditional approaches to cointegration, structural break in time series can be checked
by Chow test. In ARDL, the CUSUM and CUSUMsq tests provide diagnosis for such
information. For example, in Fig I and II, if the blue lines cross the red lines then
structural break is likely. Based on the results obtained of this study, such outcome is
unlikely. Also ARDL bounds test approach applies notwithstanding ambiguity in the
order of integration7. This issue is relevant because in the presence of structural break in
the data generating process, the traditional approaches may not capture cointegrating
7 The ARDL approach for cointegration has information about structural break in time series data as it’s a
nature of developing economies (Wahid and Shahbaz, 2009 and Shahbaz, 2009)
13
relation. This can potentially affect the outcome of the unit root test and the predictive
powers (Leybourne and Newbold 2003; Perron, 1989, 1997)8. The ARDL approach is
implemented by the following unrestricted error correction method (UECM) form (See
Pesaran et al. 2001, page-292)
[ ] tit
p
iit
p
itt LINFLUNPLINFLUNPtLINF ηλλαααα +
∆+∆++++=∆ −
=−
=−− ∑∑
1
2
0
1141321 (3)
In Equation-3, 3α and 4α , the long run parameters show partial impact on the dependent
variable. The 21,λλ refer to the short run parameters, 1α , 2α and refer to intercept and
the coefficient of time trend respectively, and η is the error term. The null hypothesis of
no cointegration is 0: 43 ==αα�
H against the alternate 0: 43 ≠≠ ααaH . The
restrictions on UECM identify the long run relation, if any, between the series. The F-
statistic tests for joint significance for cointegration. The lower or upper bounds in small
sample is not provided in Pesaran et al. (2001), but are available in Narayan (2005).
The ARDL model calculates (p+1)k number of regressions based an appropriate number
of lags. The p indicates the number of lags in ARDL bounds testing and k is the number
of actors in the model. In selecting lags, the minimum of AIC and SBC is used. The
model has been subjected to sensitivity analysis to tests for serial correlation, functional
form, normality, White heteroscedisticity, model specification and ARCH. CUSUM and
CUSUMsq check for the stability of long and short run parameters.
4. Discussion of the Findings 8 Structural changes can happened for several reasons e.g., IMF mandated conditionalities and structural
reforms as a result of economic crises, political instability, policy regime shifts, war etc.
14
The Table-1 presents the descriptive statistics and pair wise correlation between inflation
and unemployment. The reported correlation is negative for North Cyprus.
Table-1 about here
We treat inflation and unemployment as potentially I(1); and test for non-stationarity.
Noting that the boundedness of the unemployment rate series cannot remain I(1) forever,
we recognize that use of samples in the future may produce different test results. The
same is also true for the inflation rate to some degree.
Pesaran et al (2001) critical bounds test assume that variables are stationary, I(0) or I(1);
and that none is integrated of order I(2) or higher. Formally, we apply the Augmented
Dickey-Fuller (ADF) test to check for the order of integration. Results reported in Table-
2 suggest that both the series are I(1). We choose 2 lags based on AIC and SBC. Given
the sample size, we note that the ARDL F-statistics is very sensitive to the lag. An
intercept and time trend are included following Pesaran et al., (2001).
Table-2 about here
Table-3 about here
The lag length is numbered on the first differences in the 'conditional error correction'
version of the ARDL model. The unrestricted vector auto-regression (UVAR) is used to
15
choose the maximum number of lags through Akaike information criteria (AIC). With a
selected lag length of 2 as noted earlier, the number of estimated regressions in the
ARDL model in Equation-3 is (2+1)2 = 9. The ARDL F-statistics are reported in Table-4.
The calculated F-statistics 4.329 exceeds the upper bounds at the 10 percent level when
the unemployment is the forcing variable. The same is also true when the inflation is the
forcing variable. The result suggests that the series are cointegrated, which confirms a
long run relation between the series.
Table-4 about here
4.1 Long Run Estimates from OLS, Dynamic OLS (DOLS)
The OLS estimate of (-0.7489) for the coefficient of unemployment is significant at the 1
percent level. This indicates that a trade off exists for North Cyprus. A 1 percent increase
in unemployment rate leads to an expected 0.75 percent decrease in inflation.
LUNPLINF 7489.02840.4 −=
(27.1608)* (-4.9050)*
R-squared = 0.4621 R-squared Adj = 0.4429
F-statistics = 24.0591 Durban Watson = 1.6191
The impact of lead and lag differenced terms of unemployment affect inflation rate
inversely at the 1 percent level. Inflation is influenced positively and negatively by lead
and lagged differenced terms of inflation series. The impact of lead term is positive but
16
insignificant. Inflation is inversely linked to its lagged term and significant at the 10
percent level.
1111 1375.01675.05770.05416.07467.02605.4 −+−+ ∆−∆+∆−∆−−= tttt LINFLINFLUNPLUNPLUNPLINF
(44.3742)* (-5.3889)* (-2.9928)* (-5.1757)* (1.1670) (-1.9406)***
R-squared = 0.8383 R-squared Adj = 0.7999
F-statistics = 21.7873 Durban Watson = 1.5869
[The notations *, ** and *** refer to significance at 1%, 5% and 10% level respectively.]
4.2 Short Run Regression
We examine the short run impact of unemployment rate on inflation. The term (ecmt-1)
tells us about the short run adjustment to the long run equilibrium. A significant negative
value (ecmt-1 < 0) confirms the existence of a long run relationship.
10.0257 0.3823 0.6904 tLINF LUNP ecm −∆ = − − ∆ −
(-0.1981) (-2.5153) ** (-2.9132)*
R-squared = 0.2786 R-squared Adj = 0.2231
F-statistics = 5.0221 Durban Watson = 1.8764
The coefficient of unemployment suggests that 1 percent increase in this variable reduces
the inflation by 0.3823 percent on an average, confirming trade off in the short run. The
coefficient of ECM9 is negative and significant at the 1 percent level, also confirms a
long run relation. This result also suggests convergence to the long run from the short run
9 The coefficient of ecm is -0.6904 appears high for an annual inflation.
17
deviations. The coefficient, although high, suggests that the adjustment from the short run
to long run in inflation is corrected to the tune of 69.04 % for each year. The sensitivity
tests reported in Table 2 suggest the absence of modeling problem in the short run.
4.3 Stability Tests
Following the suggestion of Pesaran et al. (2001), cumulative sum (CUSUM) and the
cumulative sum of squares (CUSUMsq) tests are performed to examine the stability of
the long-run and short run parameters. If the plots of the statistics for both tests lie within
the critical bounds set for the 5 percent level, the hypothesis, “the regression equation is
correctly specified” is not rejected (Bahmani-Oskooee and Nasir, 2004, p. 485)
Figure-1 about here
Figure-2 about here
Out results indicate that the plots of both CUSUM and CUSUMsq (Figure 1 and 2) lie
within the 5% critical bounds suggesting the model is stable and correctly specified.
5. Conclusions and Policy Implications
The paper estimates a Philips Curve for North Cyprus using ARDL bounds testing and
DOLS approaches. ADF unit root test is applied to check the order of integration. Results
establish cointegration between unemployment and inflation for North Cyprus suggesting
a long run relationship over the study period. The results from OLS and DOLS confirm
18
the tradeoff between the macroeconomic variables. The implication is that the policy
makers can use the tradeoff relation in choosing appropriate strategy. The CUSUM and
CUSUMsq tests suggest stability of the parameters.
The finding that Phillips curve exists for Cyprus and is stable opens opportunities for the
central bank to determine how best to stabilize the price level by controlling inflation and
at the same time living within an unemployment rate consistent with inflation, given that
both are undesirable outcomes. Central bank should be careful in adopting a monetary
policy that would keep inflation at a politically acceptable level. However, the stability of
Phillips curve is one side of the coin. On the other side, lies the tough choice that must be
made: Determine the sacrifice ratio for a given Phillips relation for the North Cypriots. In
terms of economic theory, the ratio must be consistent with the social welfare function.
As noted earlier, the time series properties may change over time as shocks tend to alter
behavior of economic agents. This implies that the findings hold for the period of study.
In the future, policy regime changes need to be based on further studies and other
economies bearing similar characteristics to arrive at an acceptable basis for policy.
19
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Figure 1
0
1
2
3
4
5
6
-0.4 0.0 0.4 0.8 1.2 1.6 2.0 2.4
Log
of I
nflat
ion
Relationship Between Inflation and Unemployment
Log of Unemployment
28
Table-1: Descriptive Statistics and Correlation Matrix
Variables Mean Median Max Min St.Dev Skewness LINF LUNP
LINF 3.7547 3.9607 5.3706 0.9932 0.8442 -1.3336 1.0000 -0.6798
LUNP 0.7066 0.4855 2.3025 -0.2876 0.7662 0.8613 -0.6798 1.0000
29
Table-2: Unit Root Test
Variables ADF Test at Level
T. calculated Prob. Value Lag
LINF -1.5212 0.7977 1
LUNP -0.4795 0.9785 1
ADF at 1st Difference
∆∆∆∆LINF -4.2252 0.0129 1
∆∆∆∆LUNP -4.7519 0.0039 1
Short run Diagnostic Tests
Serial Correlation LM Test = 1.5764 (0.2273)
ARCH Test = 0.7484 (0.3948)
Heteroscedisticity Test = 0.5363 (0.7103)
Jarque-Bera Test = 1.2680 (0.5304)
Ramsey Test = 0.9710 (0.3338)
30
Table-3: Lag Length Criteria
VAR Lag Order Selection Criteria
Lag LogL LR FPE AIC SC HQ
0 -50.9392 NA 0.2012 4.0722 4.1690 4.1001
1 -29.3242 38.2419 0.0520 2.7172 3.0075 2.8008
2 -22.4278 11.14045* 0.0419* 2.4944* 2.9783* 2.6337*
3 -20.6647 2.5767 0.0506 2.6665 3.3439 2.8615
4 -19.7199 1.2355 0.0662 2.9015 3.7725 3.1523
* indicates lag order selected by the criterion
LR: sequential modified LR test statistic (each test at 5% level)
FPE: Final prediction error
AIC: Akaike information criterion
SC: Schwarz information criterion
HQ: Hannan-Quinn information criterion
31
Table-4: Cointegration Test: Bounds test
Model for Estimation F-Statistics Lag
FLINF(LINF/LUNP)
FLUNP(LUNP/LINF)
4.329***
5.654**
2
2
Critical Bounds Lower bound Upper bound
1% 4.428 5.898a
%5 3.368 4.590
10% 2.893 4.008
Note: a
The critical values are from Narayan (2005) p.1990. The lag selection is based on AIC and SBC.
** and *** denotes the significant level at 0.05 and 0.10, respectively.
32
Figure-1: Plot of Cumulative Sum of Recursive Residuals
-12
-8
-4
0
4
8
12
1992 1994 1996 1998 2000 2002 2004 2006
CUSUM 5% Significance
The straight lines represent critical bounds at 5% significance level.
Figure-2: Plot of Cumulative Sum of Squares of Recursive Residuals
-0.4
0.0
0.4
0.8
1.2
1.6
1992 1994 1996 1998 2000 2002 2004 2006
CUSUM of Squares 5% Significance
The straight lines represent critical bounds at 5% significance level.